An automated system for finishing (grinding, sanding, milling etc.) of flat, contoured or complex sculptured surfaces requires a high degree of positional dexterity in the finishing equipment. Such dexterity (as found typically in industrial robots) is usually accompanied by limited absolute positional accuracy in the equipment. If finishing accuracies for the final surface are to be greater than the absolute positional accuracy of the finishing equipment, then some type of active feedback control mechanism must be implemented. This mechanism must monitor the material thickness left to be removed and thereby modify and stop the material removal process at the proper level.